Nonlinear programming approach for design of high performance sigma-delta modulators

In this chapter we present a nonlinear programming approach to the design of third-order sigma–delta modulators with respect to maximization of the signal-to-noise ratio, taking into account the modulator’s stability. The proposed approach uses an analytic formula for calculation of the signal-to-noise ratio and an analytic formula for stability of the modulator. Thus the goal function becomes maximization of the signal-to-noise ratio and constraints come from stability issues and bounds of the modulator noise transfer function coefficients. The results are compared with the optimal third-order modulator design provided by DStoolbox. The proposed procedure has low computation requirements. It is described for third-order modulators with one real pole of the loop filter transfer function and can be extended easily and generalized to higher-order modulators.